Question: System A \[ -x + 3y = -6 \\ x - 3y = -6 \] The system has no solution. The system has a…

System A \[ -x + 3y = -6 \\ x - 3y = -6 \]

The system has no solution.

The system has a unique solution: \[ (x, y) = (\boxed{\phantom{0}}, \boxed{\phantom{0}}) \]

The system has infinitely many solutions. They must satisfy the following equation: \[ y = \boxed{\phantom{0}} \]

Solution

The system of equations given is: \[ \begin{cases} -x + 3y = -6 & \\ x - 3y = -6 & \end{cases} \] First, let’s add both equations together to see if they have any solutions. Add the equations: \[ (-x + 3y) + (x - 3y) = -6 + (-6) \] This simplifies to: \[ 0 = -12 \] Since the equation \(0 = -12\) is a contradiction, the system has no solution. Thus, the correct answer is: The system has no solution.